This work presents some evidences and probable consequences of introduction of discrete medium Â the ÂCrystal WorldÂ. The ÂCrystal WorldÂ can be considered as a carrier for the fields of a matter. The given medium is believed can be considered as a set of harmonic oscillators filling all space. Discrete medium is introduced on an image and similarity of a crystalline lattice of a condensed matter. The particles - excitation are concentrated in space of a Âreciprocal lattice Â of ÂCrystal WorldÂ. This leads to the violation of the energy and momentum conservation laws at the wave number of particles higher then the wave number of the reciprocal lattice. Some possible confirmation of the given consideration may be the behavior of cosmic rays at energies higher than GZK-limit. The other possible consequences of the ÂCrystal WorldÂ approach in physics of elementary particles, cosmology, and quantum mechanics are also discussed.